Well it depends what era Mongols you are talking about. When they were split into multiple Khanates, they were a heck of a lot easier to defeat, especially when you had your own similar army base, like Timur (who defeated numerous Khans of either the Golden or White Horde, I believe). Not that nomads were impervious against them, the Qipchaqs were defeated by the Mongols, but they would certainlty have helped the Hungarians if they haden't been betrayed by the Hungarian nobles.

Counter attacks would have been extremely unwise, because their enemies always tried that. And the Mongols always were just pretending to retreat, and the enemies almost always died.

Spino, I know that the Mongols defeated the Khawarzim Empire... is it a specific battle that you are reffering to?